Formula:7749

Digital Library of Mathematical Functions ID 22.13.E5

${\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{sd}\left(z,k\right)\right)^{2}={\left(1-{k^{\prime}}^{2}{\operatorname{sd}^{2}}\left(z,k\right)\right)}{\left(1+k^{2}{\operatorname{sd}^{2}}\left(z,k\right)\right)},}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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